1. Field of the Invention
This invention relates generally to the field of hemodynamic analysis of living subjects, and particularly to an apparatus and method for non-invasively detecting and evaluating fiducial points within waveforms such as those present in the impedance cardiograms and electrocardiograms of the subject.
2. Description of Related Technology
The study of the performance and properties of the cardiovascular system of a living subject has proven useful for diagnosing and assessing any number of conditions or diseases within the subject. The performance of the cardiovascular system, including the heart, has characteristically been measured in terms of several different parameters, including the stroke volume and cardiac output of the heart.
Noninvasive estimates of cardiac output (CO) can be obtained using the well known technique of impedance cardiography (ICG). Strictly speaking, impedance cardiography, also known as thoracic bioimpedance or impedance plethysmography, is used to measure the stroke volume (SV) of the heart. As shown in Eqn. (1), when the stroke volume is multiplied by heart rate, cardiac output is obtained.
CO=SVxc3x97heart rate.xe2x80x83xe2x80x83(Eqn. 1) 
During impedance cardiography, a constant alternating current, with a frequency such as 70 kHz, I(t), is applied across the thorax. The resulting voltage, V(t), is used to calculate impedance. Because the impedance is assumed to be purely resistive, the total impedance, ZT(t), is calculated by Ohm""s Law. The total impedance consists generally of a constant base impedance, Zo, and time-varying impedance, Zc(t), as shown in Eqn. 2:                                           Z            T                    ⁡                      (            t            )                          =                                            V              ⁡                              (                t                )                                                    I              ⁡                              (                t                )                                              =                                    Z              o                        +                                                            Z                  c                                ⁡                                  (                  t                  )                                            .                                                          (                  Eqn          .                      xe2x80x83                    ⁢          2                )            
The time-varying impedance is believed to reflect the change in blood resistivity as it transverses through the aorta.
Stroke volume is typically calculated from one of three well known equations, based on this impedance change:                                           Kubicek            :                          xe2x80x83                        ⁢            SV                    =                                    ρ              ⁡                              (                                                      L                    2                                                        Z                    o                    2                                                  )                                      ⁢            LVET            ⁢                                          ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                                    ,                            (                  Eqn          .                      xe2x80x83                    ⁢          3                )                                                      Sramek            :                          xe2x80x83                        ⁢            SV                    =                                                    L                3                                            4.25                ⁢                                  Z                  o                                                      ⁢            LVET            ⁢                                          ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                                    ,                            (                  Eqn          .                      xe2x80x83                    ⁢          4                )                                                      Sramek-Bernstein                    :                      xe2x80x83                    ⁢          SV                =                  δ          ⁢                      xe2x80x83                    ⁢                                                    (                                  0.17                  ⁢                  H                                )                            3                                      4.25              ⁢                              Z                o                                              ⁢          LVET          ⁢                                                    ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                      .                                              (                  Eqn          ⁢          .5                )            
Where:
L=distance between the inner electrodes in cm,
LVET=ventricular ejection time in seconds,
Zo=base impedance in ohms,                               ⅆ                      Z            ⁡                          (              t              )                                                ⅆ                      t            max                              =              magnitude        ⁢                  xe2x80x83                ⁢        of        ⁢                  xe2x80x83                ⁢        the        ⁢                  xe2x80x83                ⁢        largest              ⁢          xe2x80x83                  xe2x80x83        ⁢                  negative        ⁢                  xe2x80x83                ⁢        derivative        ⁢                  xe2x80x83                ⁢        of        ⁢                  xe2x80x83                ⁢        the        ⁢                  xe2x80x83                ⁢        impedance        ⁢                  xe2x80x83                ⁢        change            ,                        Z          c                ⁡                  (          t          )                    ,      
occurring during systole in ohms/s,
xcfx81=resistivity of blood in ohms-cm,
H=subject height in cm, and
xcex4=special weight correction factor.
Two key parameters present in Eqns. 3, 4, and 5 above are (i)       ⅆ          Z      ⁢              (        t        )                  ⅆ          t      max      
and (ii) LVET. These parameters are found from features referred to as fiducial points, that are present in the inverted first derivative of the impedance waveform,             ⅆ              Z        ⁢                  (          t          )                            ⅆ      t        .
As described by Lababidi, Z., et al, xe2x80x9cThe first derivative thoracic impedance cardiogram,xe2x80x9d Circulation, 41:651-658, 1970, the value of       ⅆ          Z      ⁢              (        t        )                  ⅆ          t      max      
is generally determined from the time at which the inverted derivative value has the highest amplitude, also commonly referred to as the xe2x80x9cC pointxe2x80x9d. The value of       ⅆ          Z      ⁢              (        k        )                  ⅆ          t      max      
is calculated as this amplitude value. LVET corresponds generally to the time during which the aortic valve is open. That point in time associated with aortic valve opening, also commonly known as the xe2x80x9cB pointxe2x80x9d, is generally determined as the time associated with the onset of the rapid upstroke (a slight inflection) in       ⅆ          Z      ⁢              (        t        )                  ⅆ    t  
before the occurrence of the C point. The time associated with aortic valve closing, also known as the xe2x80x9cX pointxe2x80x9d, is generally determined as the time associated with the inverted derivative global minimum, which occurs after the C point, as illustrated in FIG. 1.
In addition to the foregoing xe2x80x9cBxe2x80x9d, xe2x80x9cCxe2x80x9d, and xe2x80x9cXxe2x80x9d points, the so-called xe2x80x9cO pointxe2x80x9d may be of utility in the analysis of the cardiac muscle. The O point represents the time of opening of the mitral valve of the heart. The O point is generally determined as the time associated with the first peak after the X point. The time difference between aortic valve closing and mitral valve opening is known as the isovolumetric relaxation time, IVRT. However, to date, the O point has not found substantial utility in the stroke volume calculation.
Impedance cardiography further requires recording of the subject""s electrocardiogram (ECG) in conjunction with the thoracic impedance waveform previously described. Processing of the impedance waveform for hemodynamic analysis requires the use of ECG fiducial points as landmarks. Processing of the impedance waveform is generally performed on a beat-by-beat basis, with the ECG being used for beat detection. In addition, detection of some fiducial points of the impedance signal may require the use of ECG fiducial points as landmarks. Specifically, individual beats are identified by detecting the presence of QRS complexes within the ECG. The peak of the R wave (commonly referred to as the xe2x80x9cR pointxe2x80x9d) in the QRS complex is also detected, as well as the onset of depolarization of the QRS complex (xe2x80x9cQ pointxe2x80x9d).
Historically, the aforementioned fiducial points in the impedance cardiography waveform (i.e., B, C, O, and X points) and ECG (i.e. R and Q points) were each determined through empirical curve fitting. However, such empirical curve fitting is not only labor intensive and subject to several potential sources of error, but, in the case of the impedance waveform, also requires elimination of respiratory artifact. More recently, digital signal processing has been applied to the impedance cardiography waveform for pattern recognition. One mathematical technique used in conjunction with such processing, the well known time-frequency distribution, utilizes complex mathematics and a well known time-frequency distribution (e.g., the spectrogram). See for example, U.S. Pat. Nos. 5,309,917, 5,423,326, and 5,443,073 issued May 10, 1994, Jun. 13, 1995, and Aug. 22, 1995, respectively, and assigned to Drexel University. As discussed in the foregoing patents, the spectrogram is used for extraction of information relating to the transient behavior of the dZ/dt signal. Specifically, a mixed time-frequency representation of the signal is generated through calculation of the Fast Fourier Transform and multiplication by a windowing function (e.g., Hamming function) to convert the one-dimensional discrete dZ/dt signal into a two-dimensional function with a time variable and frequency variable.
However, the spectrogram (and many of the time-frequency distributions in general) suffers from a significant disability relating to the introduction of cross term artifact into the pattern recognition calculations. Specifically, when a signal is decomposed, the time-frequency plane should accurately reflect this signal. If a signal is turned off for a finite time, some time-frequency distributions will not be zero during this time, due to the existence of interference cross terms inherent in the calculation of the distribution.
Another limitation of the spectrogram is its assumption of stationarity within the windowing function. This assumption is valid if the frequency components are constant throughout the window. However, biological signals, including the ECG and the impedance waveform, are known to be non-stationary.
Additionally, the signal processing associated with such time-frequency distributions by necessity incorporates complex mathematics (i.e., involves operands having both real and imaginary components), which significantly complicates even simple pattern recognition-related computations.
Furthermore, such prior art empirical and time-frequency processing techniques impose substantial filtering requirements which can be restrictive in terms of hardware implementation. For example, the time delay associated with xcex94Z waveforms may be large due to factors such as sharp frequency cutoffs required for empirical fiducial point detection.
Based on the foregoing, what is needed is an improved method and apparatus for assessing hemodynamic parameters, including cardiac output, within a living subject. Such method and apparatus would ideally be completely non-invasive, accurate, easily adapted to the varying physiology of different subjects, and would produce reliable results under a variety of different operating conditions. Additionally, such improved method and apparatus would be based on comparatively simple mathematical operations and non-imaginary operands, thereby reducing the burden on associated signal processing hardware and software. Ideally, the effects of other potential sources of error (such as respiratory artifact) would also be mitigated or eliminated.
The present invention satisfies the aforementioned needs by an improved method and apparatus for non-invasively assessing hemodynamic parameters, including cardiac output, within a living subject.
In a first aspect of the invention, an improved method of determining at least one hemodynamic parameter associated with a living subject is disclosed. In one exemplary embodiment, the hemodynamic parameter comprises cardiac output, and the method comprises providing a plurality of electrodes disposed relative to the thoracic cavity of the subject; measuring at least one impedance waveform associated with the thoracic cavity using at least one of the plurality of electrodes; processing at least one impedance waveform using wavelet transforms to identify one or more fiducial points within the impedance waveform; and determining cardiac output based at least in part on the one or more fiducial points. Rather than using prior art empirical curve fitting or time-frequency distributions, the fiducial points of the xcex94Z and dZ/dt waveforms (e.g., B, C, X, and O) are detected in the present invention using discrete wavelet transforms. The difference between each detected X and B point is used in the present embodiment to calculate ventricular ejection time (LVET). The magnitude of the largest negative derivative of the impedance change occurring during systole (dZ/dtmax) is calculated from the C point. LVET and dZ/dtmax are then used to calculate the stroke volume, from which cardiac output is derived.
In contrast to the extensive processing and complex mathematics associated with the prior art time-frequency method, the wavelet transform methodology of the present invention advantageously requires only simple additions and multiplications of real numbers, thereby substantially simplifying the processing associated with the cardiac output (CO) determination. Furthermore, cross terms are minimized as part of the wavelet transform methodology of the present invention, thereby increasing the accuracy of the CO determination.
In a second aspect of the invention, a method of detecting specific events within a second hemodynamic parametric waveform is disclosed. In one exemplary embodiment, the second waveform comprises the electrocardiogram (ECG) of the subject, the specific events comprise individual xe2x80x9cbeatsxe2x80x9d of the subject""s cardiac muscle, and the method comprises measuring at least one ECG waveform using at least one of the plurality of electrodes; processing the at least one waveform using discrete wavelet transforms to identify one or more fiducial points within the ECG; identifying one or more QRS complexes based at least in part on the one or more fiducial points; and identifying beats based at least in part on the identified QRS complex(es). The peak of the R wave (R point) in the QRS complex as well as the onset of depolarization of the QRS complex (Q point) are also detected. The time interval between the R waves is also used to calculate the heart rate.
In a third aspect of the invention, an improved computer program for implementing the aforementioned methods of hemodynamic parametric assessment (e.g., determination of cardiac output from the impedance waveform, and identification of cardiac beats within the ECG) using discrete wavelet transforms is disclosed. In a first exemplary embodiment, the computer program comprises an object code representation of an assembly language source code listing, the object code representation being disposed on a transportable storage medium (e.g., floppy disk). In a second embodiment, the computer program is disposed on the discrete storage device of a signal processing apparatus and adapted to run on the digital processor thereof. The computer program further comprises a graphical user interface (GUI) operatively coupled to the display and input device of the signal processing apparatus. One or more subroutines or algorithms for implementing the discrete wavelet transform and fiducial point detection methodologies of the invention are included within the program. In a third exemplary embodiment, the computer program comprises an instruction set disposed within the storage device (such as the embedded program memory) of the digital signal processor (DSP) of the signal processing apparatus.
In a fourth aspect of the invention, an improved apparatus for assessing one or more hemodynamic parameters associated with a living subject is disclosed. In one exemplary embodiment, the hemodynamic parameter under evaluation comprises the cardiac output of the subject, and the apparatus generally comprises a plurality of electrodes disposed in proximity to the thoracic cavity of the subject; a current source adapted to provide a predetermined current through the thoracic cavity of the subject via at least one of the plurality of electrodes; and a signal processing apparatus adapted to analyze the signals obtained from the electrodes and determine stroke volume (and accordingly cardiac output) therefrom. The signal processing apparatus comprises a signal conditioning apparatus adapted to process signals (including the impedance signal(s) and ECG derived from one or more of the electrodes) and produce conditioned signals relating thereto; and a processor adapted to detect the fiducial points within the impedance signal(s) or conditioned signals using discrete wavelet transforms, from which cardiac output is ultimately determined.
In one variant, the apparatus further comprises an analog-to-digital converter which converts the analog signals to a binary digital format for use by the processor, the processor comprising a digital signal processor (DSP) adapted to run one or more of the aforementioned fiducial point detection computer programs thereon. The apparatus also includes a random access memory (RAM) or other storage device in data communication with the processor for storing data prior to and/or after processing by the processor.
In a fifth aspect of the invention, an improved method of providing treatment to a subject using the aforementioned cardiac output assessment methodology is disclosed. The method generally comprises the steps of: disposing a plurality of electrodes with respect to the thoracic cavity of the subject; measuring the impedance and ECG data of the subject non-invasively; determining the stroke volume of the subject""s cardiac muscle during at least one cardiac cycle using discrete wavelet transforms; determining the cardiac output of the subject based at least in part on the stroke volume, and providing treatment to the subject based on the determined cardiac output.